In order to have a good performance for maneuvering target tracking, a genetic interacting multiple model (GIMM) algorithm based on the $H_{infty}$ filter is proposed in this paper. It introduces the $H_{infty}$ filter as model-conditional filter, which keeps its robustness by constantly adjusting parameters, to improve the performance and the precision. Meanwhile, it optimizes model probabilities using the genetic algorithm (GA), chooses sub-models which are close to true models from a set of models, adjusts the number of models and parameters in real-time, reduces excessive competition, and improves the performance of the algorithm. The simulation results indicate that, the algorithm has higher tracking accuracy and stronger robustness than the standard IMM algorithm.